Pairing in a tight-binding model with occupation-dependent hopping rate: exact diagonalization study

H.Q. Lin and J.E. Hirsch, Phys. Rev. B 52, 16155 (1995).

The Hubbard model with occupation-dependent hopping rate exhibits superconductivity in a wide range of parameters within mean field (BCS) theory. Here we study pair binding energies in this model for small clusters by exact diagonalization of the Hamiltonian. The model is defined by on-site and nearest neighbor repulsions $U$ and $V$, and occupation-dependent hopping rate $t(n)=t+n\Delta t$. We present results for one-dimensional chains and for two-dimensional square lattices of sizes $4\times 4$, $6\times 6$ and $8 \times 8$. As a function of carrier density $n$ the pair binding energy first increases and then decreases, and vanishes beyond a critical density. BCS results for the pair binding energy are found to be in remarkably good agreement with the exact results. In particular, BCS theory accurately reproduces the range of interaction parameters where pair binding exists in the exact solution. The model is found to exhibit no tendency to phase separation or clustering of more than two particles even for parameters giving rise to strong pair binding, in contrast to other tight binding models where pairing occurs.